Magnetic properties of cuprate superconductors based on a phase separation theory

There is a great debate concerning the hole of the inhomogeneities in high critical temperature superconductors (HTS). Several experiments indicate a possible electronic phase separation (PS). However, there is not a method to quantify how such transition occurs and how it develops. Here we show that the Cahn-Hilliard (CH) theory of phase separation provides a way to trace the phase separation process as a function of temperature. We connect these calculations with the Bogoliubov-deGennes (BdG) approach to an inhomogeneous superconductor and derive many HTS properties of the La_2-xSrCuO₄ (LSCO) system. The results yield: an onset of superconductivity that follows close the Nernst signal, the leading edge shift is close to the zero temperature average gap, and the superconducting phase is achieved by percolation. Our approach reproduces also the experimental measurements of the H_c2 field